44 A. Gabibov et al.“closed ribbon”. Here by the termladderwe assume the lattice surface where
the points (nucleotides) are located on the boundary curves and connected
by edges (phosphodiester bonds). These edges may be disrupted. From the
chemical point of view, the substrates and products during the DNA topoi-
somerisation are identical and the catalytic events result in small topological
changes. The product from the previous single turnover will play the role of
the substrate in the next stage. So the ensemble of topoisomers exists at each
step of the reaction. Even a single catalytic event results in the quantum leap
in the scDNA topology. This allows study of most of biocatalytic problems of
DNA supercoiling within the frame of the problems of DNA topology, DNA
hydrodynamics and statistics of biopolymers. The general scheme of enzyme-
mediated topological transformations of DNA is displayed in Fig. 4.1.
DNA molecule runs a whole sequence of the states, from a supercoiled one
to the relaxed one. Moreover, either of those steps could be reversible.
In this connection, to describe kinetics of DNA relaxation correctly it is
necessary:(a) To possess information about the instant concentrations of either of the
topoisomers involved in the reaction.
(b) To identify integral index as a function of these concentrations and
reflecting the reaction turnover.
Fig. 4.1.Mechanisms of enzyme-mediated DNA relaxation. (a) Topoisomerase I-3′.
(b) Topoisomerase II. Two possible ways of topoisomerase action, distributive and
processive kinetic schemes (see text for details)